This study describes a new technique of unsupervised domain adaptation based on eigenanalysis in kernel space, for the purpose of categorisation tasks. The authors propose a transformation of data in source domain, such that the eigenvectors and eigenvalues of the transformed source domain become similar to that of the target domain. They extend this idea to the reproducing kernel Hilbert space, which enables to deal with non-linear transformation of source domain. They also propose a measure to obtain the appropriate number of eigenvectors needed for transformation. Results on object, video and text categorisations tasks using real-world datasets show that the proposed method produces better results when compared with a few recent state-of-art methods of domain adaptation.